Measure a Fairyʼs Height — First Research
by Scorpy-l
Summary: It is possible to study fairies. My first article is about a fairyʼs height. I strongly recommend you to read the full colorful version with pictures. The link is right at the beginning.


**IMPORTANT NOTE!**

There is a full version of this article with pictures. You may leave a review here but please read the full colorful version. This is the link (sorry, you❜ll have to retype it in your browser):

 **tinyurl** **.**

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 **fairy-research-1**

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— I thought… this is a fairy-tail..

— It is. But so what? Since this is a fairy-tail, what makes you think that the laws of physics stop working here? Imagine what would happen in a fairy-tail world if gravity would not work there. What about friction? Or if solar energy wouldn❜t warm up Earth! Are aerodynamic laws any different in that sense?❞

 _Yury Nesterenko,  
_ ❝ _A Hero, a Dragon and a Princess_ ❞

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 **Measure a Fairy** ❜ **s Height**

 **First Research**

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 **It is possible to study fairies**

Do you remember the scene from ❝The Great Fairy Rescue❞ when Lizzy writes carefully on the notebook❜s cover: ❝Scientific Fairy Research.❞ That is not an oxymoron at all! Science lets us study anything that exists, and in Lizzy❜s world there exists not just people and animals but all kind of creatures—even warty trolls and fairies. Let us try to write a real scientific article about fairies. It looks like there are no fairies in our world, so we❜ll limit ourselves to characters in Disney movies.

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 **It is interesting for a viewer and helpful for an author**

Imagine our characters changing their size from scene to scene. Now Tink is no bigger than a match box while in the next scene she is unable to fit inside a big cup. To avoid such absurdity, the creators of animated movies make sure they know exactly how tall every character is.

A fairy❜s weight is important as well. An animator has to make the character❜s movement both graceful and plausible. To achieve that it is important to consider the weight of every object the characters interact with. Otherwise the scene will never appear convincing. It is helpful both professional screenwriters and fans to ask: ❛How much does a fairy weigh? Otherwise we might, in one moment, ruin the thrill and suspense with an awkward scene.❜

For one of my stories, I had to calculate a fairy❜s weight because that was the question of her life and death. The outcome wasn❜t good enough for me, so the scene was deleted. However, thanks to that we have got a great opportunity to calculate the weight of a fairy.

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 **Premise and Tasks**

Certainly, we can not determine an exact value to tenth decimal digit, simply because the authors themselves could easily distort the proportions for artistic reasons. Rather, we shall try to find some general plausible values. It is doubtful that Walt Disney Studio would share a 3D-models with us; hence why we shall use basis frames from animated movies.

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 **A Fairy** ❜ **s Height**

 **Secondary Sources**

Let us begin by taking a look at the height of a fairy. It is possible that some Tinkerbell fans have already calculated everything. I asked Google for _Disney fairy height_ and _Tinkerbell_ _s height_ and got nothing but some answers on forums that began as: ❝I think… Probably…❞. The only plausible value I could find was in the following page:

 **[LINK]** wiki/Never_Fairies

❝The average Never fairy stands at five inches tall (12.7 cm).❞

Unfortunately, the authors were not kind enough to explain how did they come to that conclusion of 12.7 centimeters. Were they lucky enough to measure two hundred living fairies and then calculated the median? Let us try to confirm or disprove this assumption. Pictures from the movies will help us to do that. First, let me show you how we shall measure the length in a frame.

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 **That is How We Measure**

1\. Yellow pencil❜s length is 174.7 mm.

2\. Let us draw a transparent rectangle on top of it. Its size should be just right to match the yellow pencil❜s length.

3\. We decrease the size of the second rectangle to make it as long as the second pencil. Take notes, how much does the rectangle change. In our case its scale is 73.37 percent. Now we solve the simplest proportion and get 128.17 mm.

As you see, the error is less than one percent. If I were using a long-focus objective and a tripod, and if I had measured the length by a fractions of a pixel, then the error would have been even less. The point is that the method is working and it is good enough for our purpose.

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 **Primary Sources**

On this picture we can clearly see a ❝Bicycle❞ playing card. Its width is not constant (playing cards for bridge are slightly wider) but its height is always 88,9 mm. Out of curiosity I found an old playing card in my drawer (manufactured by a different company) and measured it as well. This one❜s height was 91 mm.

Measuring error of a fairy is significant. Tink bent her legs and she is lying not quite parallel to the card (well, she couldn❜t lie in a different way). However, now we know for certain that a fairy❜s height is more that 90 mm.

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 **A fairy** ❜ **s height is more that 90 mm.**

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We shall skip the frames in which Tink was sitting on a thimble and when she runs on the piano keys. Thimbles are different and we have to draw many overlapped parts—the error becomes way to big. It is even worse with the piano keys: the scene is dark, motion blurred and we have no idea what piano might have been on a wrecked pirate ship. The size of keys is different depending on manufacturer (let alone we have a no-name piano from 19th century).

Let❜s go to some other frames that give us better understanding of how tall fairies actually are.

Stamps are a great reference point! I saved the frame with a picture of the South Wales stamp, corrected its proportions as good as I could and I asked a search engine to find it. Google was kind enough to give me some pictures with excellent quality.

It was challenging however to find an exact measure of the stamp. According to Wikipedia, stamps are usually 10 to 30 millimeters wide or tall. That❜s not good enough for us. I would gladly measure the stamp if I had it. Unfortunately, they❜re not so easy to buy. Also keep in mind that our research isn❜t supported by any sponsors (at least for now). Suddenly it hit me: what if I could find a scanned stamp (rather than a photo), would it be possible then to find out its original size? Sure! To do so, I❜d need to know the resolution the stamp was scanned with. Fortunately, I could find such picture.

(Many thanks to a stamp collector who did not erase the metadata in the file!) The resolution is perfect for printing (300 dots per inch). Though an experienced philatelist would be shocked by the texture artists❜ work. Just take a look at how terribly the stamp is squashed in the frame. The sad thing is that if the 3D artists did a sloppy job with texturing, who knows how much the proportions of other objects and characters might be distorted as well.

Let us assume that the stamp❜s height is correct while its width is distorted. If we assume the opposite, then Tink❜s height would be less than 80 mm. Since it contradicts our observations, it looks like our first assumption makes more sense. Our next value is **102,8 mm** (plus or minus, because we should take her pose into account). We❜ll keep the measurement. By the way, look at the tinker❜s thin neck. That❜s another indirect clue that our fairy is very small, otherwise because of the weight distribution she would move clumsily (her head would change the balance).

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 **A fairy** ❜ **s height is approximately 100 mm.**

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Now let us get to the scene in which Tink shows Lizzy how fairies live and how they help nature. We can see the tinker in front of a kerosine lamp, scissors, crayons, stale and even a ruler. By mischance, it faces down the scale. The very next scene, however, is quite helpful.

As a rule, a new pencil❜s length is exactly 175 mm. If that is the case, then Tink❜s height is just 91.7 mm. One millimeter more than a playing card. Obviously, that❜s something wrong here.

First, what makes us think that Lizzy❜s pencil is 175 mm? She could draw with it for a while and the pencil would become shorter. But then the fairy❜s height must be even smaller! What if we measure the pencil❜s thickness first and calculate the proportion? Sure!

Yes, Lizzy, I am astonished just like you. A pencil❜s thickness is usually 6 mm. Therefore, the pencil❜s length from the frame should be 102 mm, right? Something is definitely going wrong here. Alright, and what if the pencil is actually thicker than it appears? It makes the picture even worse, because it must be at least 10 mm thick, so it could be 175 mm long. Why our measurements do not add up?

Possible reasons:

1\. The pencil is actually either too thick or too long.

2\. The pencil and Tink are not on the same distance from the camera and we❜ll get distortions because of perspective, therefore the measurements are incorrect.

3\. Tink❜s height is approximately 90 mm.

It is certainly possible that Lizzy has a special pencil (there are large souvenir pencils for example) and the objects are not on the same distance from the camera. Anyway, it appears that in this scene Tink❜s height is approximately 90 mm.

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Now comes the most important frame. This picture will be especially useful for our next article in which we❜ll try to weigh a fairy. But even now the ruled album will help us to find the height of our little tinker.

As you see, the album is uneven and we see it not quite from the top. Otherwise it would look very boring. I❜ll do the match moving to remove the perspective distortions. What is match moving anyway? Imagine a white space and a little black ball. Obviously there are infinitely many ways to place the camera but still take a picture of the ball so it appears in the same place on the frame. Let us add a second ball, then the third one, one more (in practice artists usually use at least ten). Now we can not take a shot of the balls from another point in space and get the same picture. That means, we have found the only possible point in space where the camera must be.

In our case we do not have any black balls. The only reference we can use is these tiny scratches and dark spots on the paper. I spent quite a bit of time trying to track the correct position of the camera in space. It is a shame that Lizzy❜s dad did not give her a checked album with a rough paper texture.

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Yes! The camera is tracked! Now I need only three points to build a plane. The next step is a bit tricky.

Imagine our camera turning into a projector. The frame we saw is being projected on the plane. We know already that the plane is placed on a correct angle. Imagine us using a real camera looking at the album on the table. Now, after projecting the picture back on a correctly oriented plane we could eliminate the distortions of perspective. Well, mostly.

Since the album is not an ideal plane, we can correct the rest of distortions in a graphic editor.

All we should do now is to find out how big Lizzy❜s drawing actually is. Fortunately, we have a great reference here—the rules. Let us assume that texture artists did their job properly and used the correct standards.

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 **[LINK]** wiki/Ruled_paper#Regional_standards

The problem is that the standards are different depending on the country. How can we find out what rules do we have in our case? Let us take a look at the album right from the top:

We are lucky because the perspective distortions are negligible here. The distance between the rules in the album are almost equal to the thickness of the pencil or to be precise a wax crayon. Unfortunately, I could not find the crayons with the trademark from the movie. Maybe the authors made it up or it is not very popular. That is why we shall take the ❝Crayola❞ crayons for comparison.

products/crayola-crayons/

If the data is correct, the size of a crayon is 92 × 8 mm. That means, that the distance between rules are either 8 mm (if the thickness is correct) or 12.59 mm (if the length is right).

Let us take a look at the standards used for making wide ruled copy books. As things turn out, one have to pay from 27 to 40 euros to read the standard DIN 16552:1977-04 (and its later versions). As I have already mentioned, our research is not sponsored for now. Let us find some open sources then:

 **[LINKS]**.ru/files/gost/gost_

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There is a reason to assume that the distance between the rules is 8—8.7 mm. Finally, we can measure Tink using this data. We get 81—88 mm. Does it mean that we made a mistake or a fairy❜s height is approximately 88 mm?

Let us find the median of our collected data:

(114 + 102.8 + 90 + 88) : 4 = 98.7 mm.

What conclusion should we make?

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 **A fairy** ❜ **s height is approximately 10 cm.**

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It looks like our colleagues from the Wiki about fairies were wrong. They have definitely overestimated the little tinker❜s height. Granted our data contained errors (because some artists do not double check the proportions) but we could get a plausible value and we have just measured a fairy!

Next time we shall use this value and find out how much a young little artisan weighs.

/z5maykn


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